# 3428. EvenOdd

Consider the following function $f(X)$, which takes a single positive integer as argument, and returns an integer.

function f(X):
iterations := 0
while X is not 1:
if X is even:
divide X by 2
else:
return iterations


It can be shown that for any positive integer $X$, this function terminates.

Given an interval $[L, R]$, compute the sum

$$S = f(L) + f(L+1) + \cdots + f(R-1) + f(R)$$

### 输入格式

The first and only line of input contains two integers $L$ and $R$ ($1 \leq L \leq R \leq 10^{18}$).

### 输出格式

Output the result $S$ modulo the prime $10^9+7$.

### 样例

Input
1 127

Output
1083

Input
74 74

Output
11


12 人解决，21 人已尝试。

14 份提交通过，共有 74 份提交。

6.4 EMB 奖励。